Complement

From Compsci1

COMPLEMENT

We use complement to help store negative numbers in the computer. We use + and – to mark positive and negative numbers. However, computers can only read information in bits, 0s or 1s, so we use a new method to store negative numbers.

The 1’s complement (ones complement) of a binary numbers is found by changing all the 1s to 0s and all the 0s to 1s.
			1001 0011
1s complement	0110 1100

The 2’s complement (twos complement) of a binary number is found by getting the ones complement first and then adding 1.

EG:
Binary number		1100 0101
1’s complement		0011 1010
					+  1
				_______
2’s complement		0011 1011

Negative numbers are the 2’s complement of the corresponding positive number.  To subtract a number, find the 2’s complement and add it.

Sign bit:
The left most bit of a binary number is the sign bit:
0	means the number is positive
1	means the number is negative.

Twos complement overflow flag: If we add or subtract numbers and part of the answer overflows the available capacity of the storage space this can cause a problem. If we add 2 negative numbers in twos complement the answer can overflow beyond the capacity and give the impression of a positive number. To catch this problem the computer has the TWOS COMPLEMENT OVERFLOW FLAG which can be written into a program and checked after an operation to see if this has happened.